Somewhat true. In "winner takes all" naturally the asymptotic end point is that all the wealth is on one agent at a time, and it is passed around in transaction

Somewhat true. In "winner takes all" naturally the asymptotic end point is that all the wealth is on one agent at a time, and it is passed around in transactions randomly. It would be more interesting to look at where the agents end up from their starting positions. Besides looking at wealth inequality, one could look at "consistency" or whatever you call it.